Abstract

For the nonsingular, non-Hermitian and positive semidefinite linear systems, we derive the convergence results of the single-step preconditioned HSS (SPHSS) method under suitable constraints. Additionally, we consider the acceleration of the SPHSS method by Krylov subspace methods and some spectral properties of the preconditioned matrix are established. Numerical experiments are presented to further examine the effectiveness of the proposed method either as a solver or a preconditioner.

Keywords

Supported by National Key Research and Development Program of China (2018YFC0603500) and National Science Foundation of China (41725017). It is also partially supported by the CAS/CAFEA international partnership Program for creative research teams (Nos. KZZD-EW-TZ-19 and KZZD-EW-TZ-15).